CONSISTENCY OF OBJECTIVE BAYES FACTORS AS THE MODEL DIMENSION GROWS

• 成果类型: Article
• 署名作者: Moreno, Elias; Javier Giron, F.; Casella, George
• 署名单位: University of Granada; Universidad de Malaga; State University System of Florida; University of Florida
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS754
• 发表日期: 2010
• 页码: 1937-1952
• 关键词: VARIABLE SELECTION

摘要

In the class of normal regression models with a finite number of regressors, and for a wide class of prior distributions, a Bayesian model selection procedure based on the Bayes factor is consistent [Casella and Moreno J. Amer Statist. Assoc. 104 (2009) 1261-1271]. However, in models where the number of parameters increases as the sample size increases, properties of the Bayes factor are not totally understood. Here we study consistency of the Bayes factors for nested normal linear models when the number of regressors increases with the sample size. We pay attention to two successful tools for model selection [Schwarz Ann. Statist. 6 (1978) 461-464] approximation to the Bayes factor, and the Bayes factor for intrinsic priors [Berger and Pericchi I. Amer Statist. Assoc. 91 (1996) 109-122, Moreno, Bertolino and Racugno J. Amer Statist. Assoc. 93 (1998) 1451-1460]. We find that the the Schwarz approximation and the Bayes factor for intrinsic priors are consistent when the rate of growth of the dimension of the bigger model is O(n(b)) for b < 1. When b = 1 the Schwarz approximation is always inconsistent under the alternative while the Bayes factor for intrinsic priors is consistent except for a small set of alternative models which is characterized.